In [56]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import pmdarima as pm
from statsmodels.tsa.arima_model import ARIMA
from sklearn.metrics import mean_squared_error
from math import sqrt, ceil

sns.set_theme()

Temporal Modelling (ARIMA)¶

In this notebook we apply an ARIMA model to the 3 datasets, and attempt to predict the last 30 days in the dataset. First we define the fitting and plotting functions we will use for all datasets. We utilize the pmdarima package for fitting and forecasting, and Seaborn for plotting the results.

In [61]:
def autoARIMAfunc(df):
    
    # Training data split
    train_df = df.iloc[:-30]  
    test_df = df.iloc[-30:]
    
    # define output dataframes
    forecast_df = pd.DataFrame(index = test_df.index)
    upper_df = pd.DataFrame(index = test_df.index)
    lower_df = pd.DataFrame(index = test_df.index)
    fit_df = pd.DataFrame(index = train_df.index)
    
    columns = df.columns
    for col in columns[1:]:
        # apply auto_arima. will estimate the pdq x PDQ model paramenters
        model = pm.auto_arima(train_df[col], seasonal=True, start_p=0, start_q=0, max_p=10, max_q=10, trace=True)
        # generate forecast and confidence intervals
        forecast, confidenceInt = model.predict(30, return_conf_int=True)
        forecast_df[col] = forecast
        lower_df[col] = confidenceInt[:,0]
        upper_df[col] = confidenceInt[:,1]
        fit_df[col] = model.fittedvalues()
        
    return train_df, test_df, fit_df, forecast_df, lower_df, upper_df
    
In [62]:
def plotARIMAfunc(train_df, test_df, fit_df, forecast_df, lower_df, upper_df):   
    columns = train_df.columns
    k = ceil(len(columns)/2)
    fig, axs = plt.subplots(nrows=k, ncols=2, figsize=(30, k*5))
    i = 0
    j = 0
    palette = sns.color_palette()
    for col in columns[1:]:
        # Plot data and fitted model
        sns.lineplot(x = train_df.timestamp.iloc[-300:], y = train_df[col].iloc[-300:], ax=axs[i,j], color=palette[0], label="Actual")
        sns.lineplot(x = train_df.timestamp.iloc[-300:], y = fit_df[col].iloc[-300:], ax=axs[i,j], color=palette[1], label="Forecast")
        sns.lineplot(x = test_df.timestamp, y = test_df[col], ax=axs[i,j], color=palette[0])
        sns.lineplot(x = test_df.timestamp, y = forecast_df[col], ax=axs[i,j], color=palette[1])
        # plot confidence interval
        axs[i,j].fill_between(test_df.timestamp, lower_df[col], upper_df[col], alpha=0.2)
        
        # print RMSE, and add legend and labels
        rmse = sqrt(mean_squared_error(test_df[col], forecast_df[col]))
        print(f'RMSE for {col} Stations: {rmse}')
        axs[i,j].set_title(col + f", Forecast RMSE: {rmse}")
        axs[i,j].set_xlabel('')
        axs[i,j].set_ylabel('Energy (kWh)')
        axs[i,j].legend(loc='upper left')
        
        j += 1
        if j >= 2:
            i += 1
            j = 0
            
    plt.show()

Palo Alto¶

In [57]:
PA_data = pd.read_csv('data/EVChargingStationUsage.csv')
C:\Users\pgsva\AppData\Local\Temp\ipykernel_15248\1309580590.py:1: DtypeWarning: Columns (29,30,32) have mixed types. Specify dtype option on import or set low_memory=False.
  PA_data = pd.read_csv('data/EVChargingStationUsage.csv')
In [58]:
# format station names to merge chargers at same location
PA_data["Normalized Station Name"] = PA_data["Station Name"].str.split(pat=" / | #| [0-9]").apply(lambda col: col[1])
PA_data.dropna(subset=['Normalized Station Name'], inplace=True)
In [59]:
# transform timestamp to Datetime object and simplify to dates
PA_data = PA_data.assign(timestamp=pd.to_datetime(PA_data["Transaction Date (Pacific Time)"], format="%m/%d/%Y %H:%M", errors='coerce').dt.date)
# group energy consumption around dates and station
PA_data = PA_data[["timestamp", "Normalized Station Name", "Energy (kWh)"]].groupby(["timestamp", "Normalized Station Name"], as_index=False).sum()
# Pivot energy consumption data to have rows indexed on dates and columns indexed on stations
PA_data = pd.pivot_table(PA_data, values="Energy (kWh)", index="timestamp", columns= "Normalized Station Name", aggfunc=np.sum, fill_value=0)
PA_data.reset_index(inplace=True)

To understand the shortcomings of the datasets we identify the number of dates with no charging data for a given station

In [60]:
print(PA_data[PA_data == 0].count(axis=0)/len(PA_data.index))
Normalized Station Name
timestamp        0.000000
BRYANT           0.033382
CAMBRIDGE        0.476343
HAMILTON         0.020900
HIGH             0.027866
MPL              0.340784
RINCONADA LIB    0.418578
SHERMAN          0.994485
TED THOMPSON     0.479245
WEBSTER          0.427286
dtype: float64
In [63]:
train_df_PA, test_df_PA, fit_df_PA, forecast_df_PA, lower_df_PA, upper_df_PA = autoARIMAfunc(PA_data)
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=37372.727, Time=0.15 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=36960.169, Time=0.27 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=36146.508, Time=0.88 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=37370.730, Time=0.08 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=35994.253, Time=1.67 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=35979.611, Time=2.65 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=36761.400, Time=0.44 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=35933.462, Time=3.16 sec
 ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=36547.572, Time=0.52 sec
 ARIMA(4,1,1)(0,0,0)[0] intercept   : AIC=35900.502, Time=4.09 sec
 ARIMA(4,1,0)(0,0,0)[0] intercept   : AIC=36430.061, Time=0.82 sec
 ARIMA(5,1,1)(0,0,0)[0] intercept   : AIC=35693.881, Time=4.32 sec
 ARIMA(5,1,0)(0,0,0)[0] intercept   : AIC=36037.299, Time=0.95 sec
 ARIMA(6,1,1)(0,0,0)[0] intercept   : AIC=35440.340, Time=6.66 sec
 ARIMA(6,1,0)(0,0,0)[0] intercept   : AIC=35439.026, Time=1.60 sec
 ARIMA(7,1,0)(0,0,0)[0] intercept   : AIC=35440.092, Time=1.78 sec
 ARIMA(7,1,1)(0,0,0)[0] intercept   : AIC=35440.609, Time=5.29 sec
 ARIMA(6,1,0)(0,0,0)[0]             : AIC=35437.049, Time=0.78 sec
 ARIMA(5,1,0)(0,0,0)[0]             : AIC=36035.312, Time=0.48 sec
 ARIMA(7,1,0)(0,0,0)[0]             : AIC=35438.115, Time=0.93 sec
 ARIMA(6,1,1)(0,0,0)[0]             : AIC=35438.363, Time=3.26 sec
 ARIMA(5,1,1)(0,0,0)[0]             : AIC=35691.891, Time=1.97 sec
 ARIMA(7,1,1)(0,0,0)[0]             : AIC=35438.629, Time=2.49 sec

Best model:  ARIMA(6,1,0)(0,0,0)[0]          
Total fit time: 45.255 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=35638.486, Time=0.15 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=35263.798, Time=0.33 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=34514.366, Time=0.81 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=35636.491, Time=0.09 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=34338.900, Time=1.25 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=34318.303, Time=2.05 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=35032.734, Time=0.46 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=34295.910, Time=3.43 sec
 ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=34900.077, Time=0.56 sec
 ARIMA(4,1,1)(0,0,0)[0] intercept   : AIC=34229.779, Time=3.91 sec
 ARIMA(4,1,0)(0,0,0)[0] intercept   : AIC=34759.672, Time=0.77 sec
 ARIMA(5,1,1)(0,0,0)[0] intercept   : AIC=34049.714, Time=5.08 sec
 ARIMA(5,1,0)(0,0,0)[0] intercept   : AIC=34390.971, Time=0.91 sec
 ARIMA(6,1,1)(0,0,0)[0] intercept   : AIC=33695.646, Time=6.24 sec
 ARIMA(6,1,0)(0,0,0)[0] intercept   : AIC=33704.758, Time=1.49 sec
 ARIMA(7,1,1)(0,0,0)[0] intercept   : AIC=33688.109, Time=7.12 sec
 ARIMA(7,1,0)(0,0,0)[0] intercept   : AIC=33693.003, Time=1.46 sec
 ARIMA(8,1,1)(0,0,0)[0] intercept   : AIC=33686.721, Time=10.80 sec
 ARIMA(8,1,0)(0,0,0)[0] intercept   : AIC=33685.744, Time=2.01 sec
 ARIMA(9,1,0)(0,0,0)[0] intercept   : AIC=33684.834, Time=5.56 sec
 ARIMA(10,1,0)(0,0,0)[0] intercept   : AIC=33678.613, Time=6.95 sec
 ARIMA(10,1,1)(0,0,0)[0] intercept   : AIC=33620.929, Time=18.37 sec
 ARIMA(9,1,1)(0,0,0)[0] intercept   : AIC=33639.145, Time=15.55 sec
 ARIMA(10,1,2)(0,0,0)[0] intercept   : AIC=33621.949, Time=20.84 sec
 ARIMA(9,1,2)(0,0,0)[0] intercept   : AIC=33621.441, Time=19.53 sec
 ARIMA(10,1,1)(0,0,0)[0]             : AIC=33619.085, Time=6.95 sec
 ARIMA(9,1,1)(0,0,0)[0]             : AIC=33637.337, Time=6.73 sec
 ARIMA(10,1,0)(0,0,0)[0]             : AIC=33676.669, Time=2.96 sec
 ARIMA(10,1,2)(0,0,0)[0]             : AIC=33620.103, Time=9.77 sec
 ARIMA(9,1,0)(0,0,0)[0]             : AIC=33682.888, Time=2.57 sec
 ARIMA(9,1,2)(0,0,0)[0]             : AIC=33619.492, Time=9.45 sec

Best model:  ARIMA(10,1,1)(0,0,0)[0]          
Total fit time: 174.174 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=34402.789, Time=0.17 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=33665.912, Time=0.29 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=32640.865, Time=0.81 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=34400.789, Time=0.08 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=32617.529, Time=1.47 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=32618.308, Time=2.11 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=32644.473, Time=2.37 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=32617.125, Time=1.37 sec
 ARIMA(0,1,3)(0,0,0)[0] intercept   : AIC=32619.060, Time=2.61 sec
 ARIMA(1,1,3)(0,0,0)[0] intercept   : AIC=32621.084, Time=4.25 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=32615.139, Time=0.70 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=32638.880, Time=0.33 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=32642.488, Time=1.19 sec
 ARIMA(0,1,3)(0,0,0)[0]             : AIC=32617.074, Time=1.04 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=32615.543, Time=0.64 sec
 ARIMA(1,1,3)(0,0,0)[0]             : AIC=32619.114, Time=1.59 sec

Best model:  ARIMA(0,1,2)(0,0,0)[0]          
Total fit time: 21.043 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=38294.451, Time=0.18 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=37766.676, Time=0.28 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=36777.417, Time=0.82 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=38292.451, Time=0.06 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=36708.879, Time=1.49 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=36691.628, Time=2.37 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=37466.409, Time=0.45 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=36678.557, Time=3.15 sec
 ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=37270.389, Time=0.53 sec
 ARIMA(4,1,1)(0,0,0)[0] intercept   : AIC=36665.539, Time=4.72 sec
 ARIMA(4,1,0)(0,0,0)[0] intercept   : AIC=37178.309, Time=0.79 sec
 ARIMA(5,1,1)(0,0,0)[0] intercept   : AIC=36581.019, Time=5.09 sec
 ARIMA(5,1,0)(0,0,0)[0] intercept   : AIC=36885.907, Time=0.97 sec
 ARIMA(6,1,1)(0,0,0)[0] intercept   : AIC=36517.437, Time=9.03 sec
 ARIMA(6,1,0)(0,0,0)[0] intercept   : AIC=36540.724, Time=1.54 sec
 ARIMA(7,1,1)(0,0,0)[0] intercept   : AIC=36466.824, Time=10.24 sec
 ARIMA(7,1,0)(0,0,0)[0] intercept   : AIC=36512.854, Time=1.66 sec
 ARIMA(8,1,1)(0,0,0)[0] intercept   : AIC=36462.998, Time=11.50 sec
 ARIMA(8,1,0)(0,0,0)[0] intercept   : AIC=36512.470, Time=1.98 sec
 ARIMA(9,1,1)(0,0,0)[0] intercept   : AIC=36443.449, Time=13.92 sec
 ARIMA(9,1,0)(0,0,0)[0] intercept   : AIC=36511.658, Time=2.72 sec
 ARIMA(10,1,1)(0,0,0)[0] intercept   : AIC=36441.011, Time=16.28 sec
 ARIMA(10,1,0)(0,0,0)[0] intercept   : AIC=36513.583, Time=2.63 sec
 ARIMA(10,1,2)(0,0,0)[0] intercept   : AIC=36435.060, Time=21.68 sec
 ARIMA(9,1,2)(0,0,0)[0] intercept   : AIC=36432.062, Time=17.62 sec
 ARIMA(8,1,2)(0,0,0)[0] intercept   : AIC=36454.681, Time=12.32 sec
 ARIMA(9,1,3)(0,0,0)[0] intercept   : AIC=36398.116, Time=21.19 sec
 ARIMA(8,1,3)(0,0,0)[0] intercept   : AIC=36450.909, Time=15.23 sec
 ARIMA(10,1,3)(0,0,0)[0] intercept   : AIC=36434.817, Time=21.26 sec
 ARIMA(9,1,4)(0,0,0)[0] intercept   : AIC=36398.719, Time=20.11 sec
 ARIMA(8,1,4)(0,0,0)[0] intercept   : AIC=inf, Time=19.21 sec
 ARIMA(10,1,4)(0,0,0)[0] intercept   : AIC=36441.275, Time=24.10 sec
 ARIMA(9,1,3)(0,0,0)[0]             : AIC=36392.599, Time=11.44 sec
 ARIMA(8,1,3)(0,0,0)[0]             : AIC=36448.939, Time=7.70 sec
 ARIMA(9,1,2)(0,0,0)[0]             : AIC=36430.020, Time=8.52 sec
 ARIMA(10,1,3)(0,0,0)[0]             : AIC=36432.887, Time=9.03 sec
 ARIMA(9,1,4)(0,0,0)[0]             : AIC=36296.187, Time=11.57 sec
 ARIMA(8,1,4)(0,0,0)[0]             : AIC=inf, Time=10.89 sec
 ARIMA(10,1,4)(0,0,0)[0]             : AIC=36439.024, Time=10.52 sec
 ARIMA(9,1,5)(0,0,0)[0]             : AIC=36222.548, Time=11.99 sec
 ARIMA(8,1,5)(0,0,0)[0]             : AIC=36247.898, Time=10.32 sec
 ARIMA(10,1,5)(0,0,0)[0]             : AIC=36220.938, Time=13.14 sec
 ARIMA(10,1,6)(0,0,0)[0]             : AIC=36214.635, Time=14.26 sec
 ARIMA(9,1,6)(0,0,0)[0]             : AIC=36230.296, Time=11.82 sec
 ARIMA(10,1,7)(0,0,0)[0]             : AIC=36207.271, Time=14.70 sec
 ARIMA(9,1,7)(0,0,0)[0]             : AIC=36196.260, Time=12.59 sec
 ARIMA(8,1,7)(0,0,0)[0]             : AIC=36151.111, Time=13.08 sec
 ARIMA(7,1,7)(0,0,0)[0]             : AIC=36134.652, Time=13.16 sec
 ARIMA(6,1,7)(0,0,0)[0]             : AIC=inf, Time=12.34 sec
 ARIMA(7,1,6)(0,0,0)[0]             : AIC=36109.126, Time=9.91 sec
 ARIMA(6,1,6)(0,0,0)[0]             : AIC=inf, Time=9.58 sec
 ARIMA(7,1,5)(0,0,0)[0]             : AIC=inf, Time=15.09 sec
 ARIMA(8,1,6)(0,0,0)[0]             : AIC=36220.666, Time=11.26 sec
 ARIMA(6,1,5)(0,0,0)[0]             : AIC=36108.985, Time=9.14 sec
 ARIMA(5,1,5)(0,0,0)[0]             : AIC=36098.519, Time=8.86 sec
 ARIMA(4,1,5)(0,0,0)[0]             : AIC=36105.079, Time=6.78 sec
 ARIMA(5,1,4)(0,0,0)[0]             : AIC=36436.173, Time=6.58 sec
 ARIMA(5,1,6)(0,0,0)[0]             : AIC=36083.979, Time=9.92 sec
 ARIMA(4,1,6)(0,0,0)[0]             : AIC=36127.976, Time=7.85 sec
 ARIMA(5,1,7)(0,0,0)[0]             : AIC=36093.608, Time=11.12 sec
 ARIMA(4,1,7)(0,0,0)[0]             : AIC=inf, Time=9.16 sec
 ARIMA(5,1,6)(0,0,0)[0] intercept   : AIC=36089.114, Time=14.21 sec

Best model:  ARIMA(5,1,6)(0,0,0)[0]          
Total fit time: 591.682 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=34346.447, Time=0.18 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=33361.909, Time=0.29 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=32491.971, Time=0.58 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=34344.447, Time=0.04 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=32493.360, Time=1.22 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=32493.403, Time=1.08 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=32495.966, Time=1.18 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=32490.031, Time=0.34 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=32491.422, Time=0.59 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=32491.465, Time=0.51 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=33359.910, Time=0.17 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=32494.026, Time=0.65 sec

Best model:  ARIMA(0,1,1)(0,0,0)[0]          
Total fit time: 6.854 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=33919.824, Time=0.13 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=33032.486, Time=0.29 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=31899.189, Time=0.68 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=33917.824, Time=0.08 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=31901.058, Time=1.36 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=31901.048, Time=1.08 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=31902.827, Time=3.14 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=31897.189, Time=0.33 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=31899.058, Time=0.55 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=31899.048, Time=0.54 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=33030.486, Time=0.17 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=31900.827, Time=1.50 sec

Best model:  ARIMA(0,1,1)(0,0,0)[0]          
Total fit time: 9.853 seconds
c:\users\pgsva\miniconda3\lib\site-packages\pmdarima\arima\auto.py:444: UserWarning: Input time-series is completely constant; returning a (0, 0, 0) ARMA.
  warnings.warn('Input time-series is completely constant; '
 ARIMA(0,0,0)(0,0,0)[0]             : AIC=-72354.931, Time=0.37 sec
Total fit time: 0.383 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=34695.447, Time=0.16 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=34461.635, Time=0.31 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=33738.856, Time=0.75 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=34693.448, Time=0.07 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=33439.533, Time=1.53 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=33377.732, Time=2.30 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=34323.820, Time=0.37 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=33257.081, Time=2.58 sec
 ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=34144.636, Time=0.50 sec
 ARIMA(4,1,1)(0,0,0)[0] intercept   : AIC=33124.355, Time=3.69 sec
 ARIMA(4,1,0)(0,0,0)[0] intercept   : AIC=33903.724, Time=0.76 sec
 ARIMA(5,1,1)(0,0,0)[0] intercept   : AIC=32845.459, Time=5.19 sec
 ARIMA(5,1,0)(0,0,0)[0] intercept   : AIC=33253.538, Time=1.03 sec
 ARIMA(6,1,1)(0,0,0)[0] intercept   : AIC=32595.793, Time=6.83 sec
 ARIMA(6,1,0)(0,0,0)[0] intercept   : AIC=32594.195, Time=1.80 sec
 ARIMA(7,1,0)(0,0,0)[0] intercept   : AIC=32595.606, Time=3.91 sec
 ARIMA(7,1,1)(0,0,0)[0] intercept   : AIC=32595.810, Time=7.93 sec
 ARIMA(6,1,0)(0,0,0)[0]             : AIC=32592.213, Time=0.92 sec
 ARIMA(5,1,0)(0,0,0)[0]             : AIC=33251.546, Time=0.57 sec
 ARIMA(7,1,0)(0,0,0)[0]             : AIC=32593.624, Time=1.87 sec
 ARIMA(6,1,1)(0,0,0)[0]             : AIC=32593.811, Time=3.54 sec
 ARIMA(5,1,1)(0,0,0)[0]             : AIC=32843.477, Time=1.99 sec
 ARIMA(7,1,1)(0,0,0)[0]             : AIC=32593.828, Time=3.36 sec

Best model:  ARIMA(6,1,0)(0,0,0)[0]          
Total fit time: 52.002 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=37001.358, Time=0.14 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=36617.960, Time=0.25 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=35738.932, Time=0.86 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=36999.362, Time=0.08 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=35602.404, Time=1.49 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=35565.158, Time=1.64 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=36392.625, Time=0.43 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=35508.874, Time=3.13 sec
 ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=36226.199, Time=0.53 sec
 ARIMA(4,1,1)(0,0,0)[0] intercept   : AIC=35409.081, Time=4.21 sec
 ARIMA(4,1,0)(0,0,0)[0] intercept   : AIC=36059.879, Time=0.77 sec
 ARIMA(5,1,1)(0,0,0)[0] intercept   : AIC=35147.057, Time=5.37 sec
 ARIMA(5,1,0)(0,0,0)[0] intercept   : AIC=35546.157, Time=1.06 sec
 ARIMA(6,1,1)(0,0,0)[0] intercept   : AIC=34925.946, Time=7.26 sec
 ARIMA(6,1,0)(0,0,0)[0] intercept   : AIC=34934.692, Time=1.58 sec
 ARIMA(7,1,1)(0,0,0)[0] intercept   : AIC=34919.316, Time=11.07 sec
 ARIMA(7,1,0)(0,0,0)[0] intercept   : AIC=34920.734, Time=1.98 sec
 ARIMA(8,1,1)(0,0,0)[0] intercept   : AIC=34891.679, Time=7.67 sec
 ARIMA(8,1,0)(0,0,0)[0] intercept   : AIC=34893.066, Time=2.70 sec
 ARIMA(9,1,1)(0,0,0)[0] intercept   : AIC=34868.841, Time=17.08 sec
 ARIMA(9,1,0)(0,0,0)[0] intercept   : AIC=34893.585, Time=2.93 sec
 ARIMA(10,1,1)(0,0,0)[0] intercept   : AIC=34861.298, Time=17.68 sec
 ARIMA(10,1,0)(0,0,0)[0] intercept   : AIC=34889.939, Time=3.91 sec
 ARIMA(10,1,2)(0,0,0)[0] intercept   : AIC=34844.542, Time=22.53 sec
 ARIMA(9,1,2)(0,0,0)[0] intercept   : AIC=34837.992, Time=20.76 sec
 ARIMA(8,1,2)(0,0,0)[0] intercept   : AIC=34895.576, Time=15.38 sec
 ARIMA(9,1,3)(0,0,0)[0] intercept   : AIC=34732.898, Time=22.98 sec
 ARIMA(8,1,3)(0,0,0)[0] intercept   : AIC=34879.929, Time=16.79 sec
 ARIMA(10,1,3)(0,0,0)[0] intercept   : AIC=34839.615, Time=23.52 sec
 ARIMA(9,1,4)(0,0,0)[0] intercept   : AIC=34755.601, Time=21.43 sec
 ARIMA(8,1,4)(0,0,0)[0] intercept   : AIC=34879.608, Time=16.50 sec
 ARIMA(10,1,4)(0,0,0)[0] intercept   : AIC=34777.824, Time=28.20 sec
 ARIMA(9,1,3)(0,0,0)[0]             : AIC=34794.968, Time=9.36 sec

Best model:  ARIMA(9,1,3)(0,0,0)[0] intercept
Total fit time: 291.312 seconds
In [64]:
plotARIMAfunc(train_df_PA, test_df_PA, fit_df_PA, forecast_df_PA, lower_df_PA, upper_df_PA)
RMSE for BRYANT Stations: 54.02127600872799
RMSE for CAMBRIDGE Stations: 64.20669476951068
RMSE for HAMILTON Stations: 6.267958501138296
RMSE for HIGH Stations: 41.74034056235554
RMSE for MPL Stations: 24.221816397569082
RMSE for RINCONADA LIB Stations: 1.3576936502378508e-05
RMSE for SHERMAN Stations: 26.62721201578065
RMSE for TED THOMPSON Stations: 30.182614413955648
RMSE for WEBSTER Stations: 43.15314186731695
No description has been provided for this image

Dundee¶

In [65]:
data_dundee = pd.read_csv('data/Dundee_merged.csv')
C:\Users\pgsva\AppData\Local\Temp\ipykernel_15248\1761076983.py:1: DtypeWarning: Columns (1) have mixed types. Specify dtype option on import or set low_memory=False.
  data_dundee = pd.read_csv('data/Dundee_merged.csv')
In [66]:
data_dundee = data_dundee.assign(timestamp=pd.to_datetime(data_dundee["End Date"]).dt.date)
data_dundee = data_dundee[["timestamp", "Address 1", "Energy(kWh)"]].groupby(["timestamp", "Address 1"], as_index=False).sum()
data_dundee = pd.pivot_table(data_dundee, values="Energy(kWh)", index="timestamp", columns= "Address 1", aggfunc=np.sum, fill_value=0)
data_dundee.reset_index(inplace=True)
In [67]:
data_dundee.head(10)
Out[67]:
Address 1 timestamp ***TEST SITE*** Charge Your Car HQ Ardler Complex, Dundee Balunie Drive, Dundee Brington Place Sheltered Housing, Dundee DCC Environment, 34 Harefield Road Dock Street, Dundee Dundee House, Dundee Dundee Ice Arena, Dundee Earn Cresent, Dundee ... Sinclair Street Sinclair Street, Dundee Social Work Building, Jack Martin Way, Dundee South Tay Street South Tay Street, Dundee Trades Lane Trades Lane, Dundee Turriff House Rannoch Road, Dundee University of Dundee, Nethergate, Dundee Whitfield Centre, Dundee
0 1970-01-01 0.0 0.00 0.00 0.00 0.00 0.000 0.00 0.000 0.00 ... 0.000 0.0 0.000 0.000 0.0 0.000 0.0 0.00 0.0 0.00
1 2017-09-01 0.0 0.00 2.08 14.06 1.36 7.623 5.72 245.582 0.00 ... 2.551 0.0 70.930 19.517 0.0 3.804 0.0 0.00 0.0 23.61
2 2017-09-02 0.0 0.00 47.17 7.69 11.17 36.744 0.00 340.500 15.13 ... 20.024 0.0 16.130 14.021 0.0 4.558 0.0 9.92 0.0 7.02
3 2017-09-03 0.0 0.00 30.94 -10.46 0.00 9.593 0.00 269.280 0.00 ... 21.638 0.0 0.000 24.964 0.0 10.384 0.0 0.00 0.0 0.00
4 2017-09-04 0.0 0.00 23.19 18.50 20.75 16.714 13.98 186.840 0.00 ... 13.448 0.0 41.036 8.362 0.0 13.136 0.0 0.00 0.0 17.08
5 2017-09-05 0.0 0.00 22.27 12.44 4.03 17.464 24.21 221.061 0.00 ... 0.563 0.0 37.220 26.702 0.0 0.000 0.0 0.00 0.0 22.65
6 2017-09-06 0.0 0.00 47.46 11.67 12.08 15.542 37.35 295.905 10.96 ... 7.973 0.0 15.410 17.055 0.0 1.800 0.0 10.15 0.0 39.93
7 2017-09-07 0.0 0.00 0.00 19.10 0.00 19.081 34.98 297.950 9.54 ... 18.134 0.0 9.800 47.267 0.0 11.660 0.0 0.00 0.0 18.52
8 2017-09-08 0.0 7.21 26.97 8.42 11.81 16.365 28.42 330.680 45.88 ... 17.007 0.0 45.470 0.000 0.0 16.669 0.0 25.55 0.0 15.32
9 2017-09-09 0.0 0.00 25.24 9.46 15.33 5.485 0.00 319.501 10.12 ... 0.000 0.0 20.900 41.381 0.0 8.049 0.0 0.00 0.0 13.00

10 rows × 35 columns

In [68]:
print(data_dundee[data_dundee == 0].count(axis=0)/len(data_dundee.index))
Address 1
timestamp                                        0.000000
***TEST SITE*** Charge Your Car HQ               0.965241
Ardler Complex, Dundee                           0.780749
Balunie Drive, Dundee                            0.259358
Brington Place Sheltered Housing, Dundee         0.042781
DCC Environment, 34 Harefield Road               0.655080
Dock Street, Dundee                              0.050802
Dundee House, Dundee                             0.296791
Dundee Ice Arena, Dundee                         0.093583
Earn Cresent, Dundee                             0.748663
Gellatly Street Car Park, Dundee                 0.008021
Greenmarket Multi Car Park, Dundee               0.010695
Housing Office East, Dundee                      0.165775
Housing Office West, Dundee                      0.165775
Janet Brougham House, Dundee                     0.427807
Lochee Charging Hub, Dundee                      0.596257
Marchbanks, Dundee                               0.216578
Menziehill House, Dundee                         0.195187
Mitchell Street, Dundee                          0.687166
Nethergate, Dundee                               0.125668
Oakland Day Centre, Dundee                       0.500000
Olympia Multi-Storey Car Park, Dundee            0.048128
Princes Street Charging Hub                      0.863636
Public Works Dept, Clepington Rd. Dundee         0.016043
Queen Street Car Park, Broughty Ferry, Dundee    0.008021
Sinclair Street                                  0.590909
Sinclair Street, Dundee                          0.967914
Social Work Building, Jack Martin Way, Dundee    0.048128
South Tay Street                                 0.566845
South Tay Street, Dundee                         0.459893
Trades Lane                                      0.580214
Trades Lane, Dundee                              0.641711
Turriff House Rannoch Road, Dundee               0.676471
University of Dundee, Nethergate, Dundee         0.556150
Whitfield Centre, Dundee                         0.109626
dtype: float64
In [69]:
train_df_dundee, test_df_dundee, fit_df_dundee, forecast_df_dundee, lower_df_dundee, upper_df_dundee = autoARIMAfunc(data_dundee)
Performing stepwise search to minimize aic
 ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=4037.793, Time=0.03 sec
 ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=3628.415, Time=0.10 sec
 ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=3769.824, Time=0.20 sec
 ARIMA(0,0,0)(0,0,0)[0]             : AIC=4044.992, Time=0.01 sec
 ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=3525.384, Time=0.16 sec
 ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=3525.115, Time=0.26 sec
 ARIMA(4,0,0)(0,0,0)[0] intercept   : AIC=3493.546, Time=0.29 sec
 ARIMA(5,0,0)(0,0,0)[0] intercept   : AIC=3482.337, Time=0.29 sec
 ARIMA(6,0,0)(0,0,0)[0] intercept   : AIC=3484.088, Time=0.35 sec
 ARIMA(5,0,1)(0,0,0)[0] intercept   : AIC=3484.143, Time=0.55 sec
 ARIMA(4,0,1)(0,0,0)[0] intercept   : AIC=3484.971, Time=0.69 sec
 ARIMA(6,0,1)(0,0,0)[0] intercept   : AIC=3485.823, Time=1.14 sec
 ARIMA(5,0,0)(0,0,0)[0]             : AIC=3482.625, Time=0.21 sec

Best model:  ARIMA(5,0,0)(0,0,0)[0] intercept
Total fit time: 4.318 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2278.628, Time=0.02 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2118.044, Time=0.08 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2040.095, Time=0.20 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2276.628, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2022.132, Time=0.14 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=2022.969, Time=0.19 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=2023.256, Time=0.21 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=2021.624, Time=0.16 sec
 ARIMA(0,1,3)(0,0,0)[0] intercept   : AIC=2023.144, Time=0.18 sec
 ARIMA(1,1,3)(0,0,0)[0] intercept   : AIC=2025.060, Time=0.47 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=2019.639, Time=0.08 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=2038.108, Time=0.06 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=2021.271, Time=0.13 sec
 ARIMA(0,1,3)(0,0,0)[0]             : AIC=2021.159, Time=0.11 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=2020.147, Time=0.07 sec
 ARIMA(1,1,3)(0,0,0)[0]             : AIC=2023.075, Time=0.30 sec

Best model:  ARIMA(0,1,2)(0,0,0)[0]          
Total fit time: 2.451 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=3142.392, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2987.076, Time=0.10 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2891.421, Time=0.13 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=3140.392, Time=0.03 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2884.857, Time=0.16 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=2885.662, Time=0.28 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=2882.518, Time=0.23 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=2886.045, Time=0.19 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=2883.839, Time=0.43 sec
 ARIMA(1,1,3)(0,0,0)[0] intercept   : AIC=2883.826, Time=0.44 sec
 ARIMA(0,1,3)(0,0,0)[0] intercept   : AIC=2886.004, Time=0.30 sec
 ARIMA(2,1,3)(0,0,0)[0] intercept   : AIC=2885.826, Time=0.74 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=2880.684, Time=0.18 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=2884.188, Time=0.10 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=2882.997, Time=0.10 sec
 ARIMA(2,1,2)(0,0,0)[0]             : AIC=2881.989, Time=0.28 sec
 ARIMA(1,1,3)(0,0,0)[0]             : AIC=2881.975, Time=0.33 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=2889.631, Time=0.05 sec
 ARIMA(0,1,3)(0,0,0)[0]             : AIC=2884.168, Time=0.18 sec
 ARIMA(2,1,1)(0,0,0)[0]             : AIC=2883.824, Time=0.19 sec
 ARIMA(2,1,3)(0,0,0)[0]             : AIC=2883.974, Time=0.47 sec

Best model:  ARIMA(1,1,2)(0,0,0)[0]          
Total fit time: 4.936 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2596.225, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2546.615, Time=0.17 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2429.353, Time=0.15 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2594.228, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2426.455, Time=0.20 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=2424.042, Time=0.34 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=2514.787, Time=0.18 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=2423.586, Time=0.28 sec
 ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=2484.064, Time=0.27 sec
 ARIMA(4,1,1)(0,0,0)[0] intercept   : AIC=2425.579, Time=0.44 sec
 ARIMA(3,1,2)(0,0,0)[0] intercept   : AIC=2425.580, Time=0.54 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=2424.261, Time=0.54 sec
 ARIMA(4,1,0)(0,0,0)[0] intercept   : AIC=2468.021, Time=0.35 sec
 ARIMA(4,1,2)(0,0,0)[0] intercept   : AIC=2423.870, Time=0.64 sec
 ARIMA(3,1,1)(0,0,0)[0]             : AIC=2421.595, Time=0.21 sec
 ARIMA(2,1,1)(0,0,0)[0]             : AIC=2422.056, Time=0.21 sec
 ARIMA(3,1,0)(0,0,0)[0]             : AIC=2482.082, Time=0.10 sec
 ARIMA(4,1,1)(0,0,0)[0]             : AIC=2423.589, Time=0.26 sec
 ARIMA(3,1,2)(0,0,0)[0]             : AIC=2423.589, Time=0.37 sec
 ARIMA(2,1,0)(0,0,0)[0]             : AIC=2512.793, Time=0.07 sec
 ARIMA(2,1,2)(0,0,0)[0]             : AIC=2422.271, Time=0.32 sec
 ARIMA(4,1,0)(0,0,0)[0]             : AIC=2466.043, Time=0.15 sec
 ARIMA(4,1,2)(0,0,0)[0]             : AIC=2421.880, Time=0.47 sec

Best model:  ARIMA(3,1,1)(0,0,0)[0]          
Total fit time: 6.319 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2828.710, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2789.673, Time=0.13 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2678.998, Time=0.13 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2826.710, Time=0.03 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2671.739, Time=0.23 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=2667.264, Time=0.26 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=2749.277, Time=0.17 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=2668.922, Time=0.35 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=2670.643, Time=0.40 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=2668.667, Time=0.25 sec
 ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=2732.319, Time=0.15 sec
 ARIMA(3,1,2)(0,0,0)[0] intercept   : AIC=inf, Time=0.87 sec
 ARIMA(2,1,1)(0,0,0)[0]             : AIC=2665.519, Time=0.20 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=2670.154, Time=0.14 sec
 ARIMA(2,1,0)(0,0,0)[0]             : AIC=2747.277, Time=0.08 sec
 ARIMA(3,1,1)(0,0,0)[0]             : AIC=2667.140, Time=0.26 sec
 ARIMA(2,1,2)(0,0,0)[0]             : AIC=2669.009, Time=0.26 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=2787.673, Time=0.07 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=2667.017, Time=0.19 sec
 ARIMA(3,1,0)(0,0,0)[0]             : AIC=2730.320, Time=0.11 sec
 ARIMA(3,1,2)(0,0,0)[0]             : AIC=inf, Time=0.80 sec

Best model:  ARIMA(2,1,1)(0,0,0)[0]          
Total fit time: 5.120 seconds
Performing stepwise search to minimize aic
 ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=2679.051, Time=0.03 sec
 ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=2679.538, Time=0.16 sec
 ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=2679.620, Time=0.11 sec
 ARIMA(0,0,0)(0,0,0)[0]             : AIC=3073.058, Time=0.02 sec
 ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=2674.738, Time=0.50 sec
 ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=2676.472, Time=0.65 sec
 ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=2676.419, Time=0.69 sec
 ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=2681.420, Time=0.22 sec
 ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=2681.184, Time=0.19 sec
 ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=inf, Time=0.87 sec
 ARIMA(1,0,1)(0,0,0)[0]             : AIC=2685.128, Time=0.15 sec

Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept
Total fit time: 3.597 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=3430.000, Time=0.02 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=3419.446, Time=0.05 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=3333.340, Time=0.16 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=3428.001, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=inf, Time=0.31 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=3290.815, Time=0.26 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=3292.769, Time=0.38 sec
 ARIMA(0,1,3)(0,0,0)[0] intercept   : AIC=3292.703, Time=0.32 sec
 ARIMA(1,1,3)(0,0,0)[0] intercept   : AIC=3283.561, Time=0.52 sec
 ARIMA(2,1,3)(0,0,0)[0] intercept   : AIC=inf, Time=1.14 sec
 ARIMA(1,1,4)(0,0,0)[0] intercept   : AIC=3273.465, Time=0.61 sec
 ARIMA(0,1,4)(0,0,0)[0] intercept   : AIC=3273.494, Time=0.41 sec
 ARIMA(2,1,4)(0,0,0)[0] intercept   : AIC=inf, Time=1.36 sec
 ARIMA(1,1,5)(0,0,0)[0] intercept   : AIC=3269.410, Time=1.05 sec
 ARIMA(0,1,5)(0,0,0)[0] intercept   : AIC=3273.751, Time=0.67 sec
 ARIMA(2,1,5)(0,0,0)[0] intercept   : AIC=inf, Time=1.59 sec
 ARIMA(1,1,6)(0,0,0)[0] intercept   : AIC=3271.147, Time=1.00 sec
 ARIMA(0,1,6)(0,0,0)[0] intercept   : AIC=3272.215, Time=0.85 sec
 ARIMA(2,1,6)(0,0,0)[0] intercept   : AIC=inf, Time=1.70 sec
 ARIMA(1,1,5)(0,0,0)[0]             : AIC=3267.453, Time=0.72 sec
 ARIMA(0,1,5)(0,0,0)[0]             : AIC=3271.792, Time=0.45 sec
 ARIMA(1,1,4)(0,0,0)[0]             : AIC=3271.506, Time=0.41 sec
 ARIMA(2,1,5)(0,0,0)[0]             : AIC=inf, Time=1.35 sec
 ARIMA(1,1,6)(0,0,0)[0]             : AIC=3269.189, Time=0.67 sec
 ARIMA(0,1,4)(0,0,0)[0]             : AIC=3271.535, Time=0.25 sec
 ARIMA(0,1,6)(0,0,0)[0]             : AIC=3270.253, Time=0.47 sec
 ARIMA(2,1,4)(0,0,0)[0]             : AIC=inf, Time=1.00 sec
 ARIMA(2,1,6)(0,0,0)[0]             : AIC=inf, Time=1.28 sec

Best model:  ARIMA(1,1,5)(0,0,0)[0]          
Total fit time: 19.083 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=3829.864, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=3806.334, Time=0.20 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=3766.022, Time=0.10 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=3827.869, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=3737.429, Time=0.24 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=3737.908, Time=0.45 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=3738.459, Time=0.29 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=3738.706, Time=0.19 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=3794.029, Time=0.28 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=3740.640, Time=0.60 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=3737.542, Time=0.18 sec

Best model:  ARIMA(1,1,1)(0,0,0)[0] intercept
Total fit time: 2.594 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2624.904, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2547.137, Time=0.10 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2448.578, Time=0.12 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2622.904, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2448.443, Time=0.20 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=2450.432, Time=0.25 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=2444.025, Time=0.22 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=2448.470, Time=0.18 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=2445.526, Time=0.28 sec
 ARIMA(1,1,3)(0,0,0)[0] intercept   : AIC=2445.577, Time=0.50 sec
 ARIMA(0,1,3)(0,0,0)[0] intercept   : AIC=2450.460, Time=0.33 sec
 ARIMA(2,1,3)(0,0,0)[0] intercept   : AIC=inf, Time=1.05 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=2442.245, Time=0.17 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=2446.728, Time=0.10 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=2446.709, Time=0.09 sec
 ARIMA(2,1,2)(0,0,0)[0]             : AIC=2443.784, Time=0.22 sec
 ARIMA(1,1,3)(0,0,0)[0]             : AIC=2443.830, Time=0.37 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=2446.763, Time=0.06 sec
 ARIMA(0,1,3)(0,0,0)[0]             : AIC=2448.723, Time=0.12 sec
 ARIMA(2,1,1)(0,0,0)[0]             : AIC=2448.703, Time=0.15 sec
 ARIMA(2,1,3)(0,0,0)[0]             : AIC=2444.812, Time=0.52 sec

Best model:  ARIMA(1,1,2)(0,0,0)[0]          
Total fit time: 5.094 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=3440.544, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=3388.836, Time=0.13 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=3268.490, Time=0.16 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=3438.554, Time=0.03 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=3265.996, Time=0.24 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=3263.760, Time=0.33 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=3328.210, Time=0.21 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=3263.456, Time=0.47 sec
 ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=3325.104, Time=0.23 sec
 ARIMA(4,1,1)(0,0,0)[0] intercept   : AIC=3258.003, Time=0.54 sec
 ARIMA(4,1,0)(0,0,0)[0] intercept   : AIC=3322.442, Time=0.30 sec
 ARIMA(5,1,1)(0,0,0)[0] intercept   : AIC=3239.231, Time=0.58 sec
 ARIMA(5,1,0)(0,0,0)[0] intercept   : AIC=3273.941, Time=0.39 sec
 ARIMA(6,1,1)(0,0,0)[0] intercept   : AIC=3236.600, Time=1.51 sec
 ARIMA(6,1,0)(0,0,0)[0] intercept   : AIC=3237.425, Time=0.54 sec
 ARIMA(7,1,1)(0,0,0)[0] intercept   : AIC=3228.405, Time=0.98 sec
 ARIMA(7,1,0)(0,0,0)[0] intercept   : AIC=3235.764, Time=0.53 sec
 ARIMA(8,1,1)(0,0,0)[0] intercept   : AIC=3229.880, Time=1.21 sec
 ARIMA(7,1,2)(0,0,0)[0] intercept   : AIC=3230.159, Time=1.36 sec
 ARIMA(6,1,2)(0,0,0)[0] intercept   : AIC=3238.272, Time=1.07 sec
 ARIMA(8,1,0)(0,0,0)[0] intercept   : AIC=3236.601, Time=0.94 sec
 ARIMA(8,1,2)(0,0,0)[0] intercept   : AIC=3230.207, Time=1.52 sec
 ARIMA(7,1,1)(0,0,0)[0]             : AIC=3226.894, Time=0.68 sec
 ARIMA(6,1,1)(0,0,0)[0]             : AIC=3234.779, Time=0.81 sec
 ARIMA(7,1,0)(0,0,0)[0]             : AIC=3233.943, Time=0.19 sec
 ARIMA(8,1,1)(0,0,0)[0]             : AIC=3228.357, Time=0.81 sec
 ARIMA(7,1,2)(0,0,0)[0]             : AIC=3228.641, Time=0.95 sec
 ARIMA(6,1,0)(0,0,0)[0]             : AIC=3235.583, Time=0.29 sec
 ARIMA(6,1,2)(0,0,0)[0]             : AIC=3236.440, Time=0.77 sec
 ARIMA(8,1,0)(0,0,0)[0]             : AIC=3234.772, Time=0.39 sec
 ARIMA(8,1,2)(0,0,0)[0]             : AIC=3228.686, Time=0.89 sec

Best model:  ARIMA(7,1,1)(0,0,0)[0]          
Total fit time: 19.082 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=3869.158, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=3826.068, Time=0.08 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=3799.768, Time=0.19 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=3867.161, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=3789.585, Time=0.24 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=3789.912, Time=0.30 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=3789.766, Time=0.36 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=3792.874, Time=0.26 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=3813.317, Time=0.18 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=3791.764, Time=0.63 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=3787.592, Time=0.12 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=3797.785, Time=0.08 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=3824.075, Time=0.04 sec
 ARIMA(2,1,1)(0,0,0)[0]             : AIC=3787.914, Time=0.21 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=3787.767, Time=0.23 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=3790.887, Time=0.12 sec
 ARIMA(2,1,0)(0,0,0)[0]             : AIC=3811.328, Time=0.11 sec
 ARIMA(2,1,2)(0,0,0)[0]             : AIC=3789.766, Time=0.43 sec

Best model:  ARIMA(1,1,1)(0,0,0)[0]          
Total fit time: 3.643 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2995.221, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2956.519, Time=0.09 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2850.400, Time=0.11 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2993.243, Time=0.03 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2841.579, Time=0.24 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=2838.389, Time=0.31 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=2921.802, Time=0.15 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=2839.670, Time=0.34 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=2837.294, Time=0.58 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=2840.097, Time=0.29 sec
 ARIMA(3,1,2)(0,0,0)[0] intercept   : AIC=2839.158, Time=0.87 sec
 ARIMA(2,1,3)(0,0,0)[0] intercept   : AIC=2843.112, Time=0.50 sec
 ARIMA(1,1,3)(0,0,0)[0] intercept   : AIC=2838.551, Time=0.46 sec
 ARIMA(3,1,3)(0,0,0)[0] intercept   : AIC=2841.268, Time=0.61 sec
 ARIMA(2,1,2)(0,0,0)[0]             : AIC=2836.114, Time=0.33 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=2839.102, Time=0.20 sec
 ARIMA(2,1,1)(0,0,0)[0]             : AIC=2837.364, Time=0.19 sec
 ARIMA(3,1,2)(0,0,0)[0]             : AIC=2837.968, Time=0.66 sec
 ARIMA(2,1,3)(0,0,0)[0]             : AIC=2800.499, Time=0.86 sec
 ARIMA(1,1,3)(0,0,0)[0]             : AIC=2837.396, Time=0.23 sec
 ARIMA(3,1,3)(0,0,0)[0]             : AIC=2840.089, Time=0.39 sec
 ARIMA(2,1,4)(0,0,0)[0]             : AIC=2798.255, Time=1.05 sec
 ARIMA(1,1,4)(0,0,0)[0]             : AIC=2838.882, Time=0.45 sec
 ARIMA(3,1,4)(0,0,0)[0]             : AIC=2800.046, Time=1.11 sec
 ARIMA(2,1,5)(0,0,0)[0]             : AIC=2798.697, Time=1.11 sec
 ARIMA(1,1,5)(0,0,0)[0]             : AIC=2841.693, Time=0.50 sec
 ARIMA(3,1,5)(0,0,0)[0]             : AIC=2800.022, Time=1.17 sec
 ARIMA(2,1,4)(0,0,0)[0] intercept   : AIC=2826.225, Time=1.38 sec

Best model:  ARIMA(2,1,4)(0,0,0)[0]          
Total fit time: 14.256 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2838.446, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2737.233, Time=0.12 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2622.442, Time=0.13 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2836.452, Time=0.03 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2624.403, Time=0.22 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=2624.404, Time=0.21 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=inf, Time=0.64 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=2620.461, Time=0.07 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=2622.420, Time=0.12 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=2622.421, Time=0.12 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=2735.241, Time=0.05 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=inf, Time=0.43 sec

Best model:  ARIMA(0,1,1)(0,0,0)[0]          
Total fit time: 2.182 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2335.577, Time=0.02 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2261.849, Time=0.11 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2229.368, Time=0.11 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2333.577, Time=0.03 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2231.014, Time=0.16 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=2231.087, Time=0.16 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=2228.849, Time=0.53 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=2230.353, Time=0.48 sec
 ARIMA(1,1,3)(0,0,0)[0] intercept   : AIC=2230.249, Time=0.43 sec
 ARIMA(0,1,3)(0,0,0)[0] intercept   : AIC=2232.208, Time=0.21 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=2230.660, Time=0.28 sec
 ARIMA(2,1,3)(0,0,0)[0] intercept   : AIC=2231.997, Time=0.73 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=2227.257, Time=0.35 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=2229.170, Time=0.08 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=2229.104, Time=0.07 sec
 ARIMA(2,1,2)(0,0,0)[0]             : AIC=2228.760, Time=0.31 sec
 ARIMA(1,1,3)(0,0,0)[0]             : AIC=2228.656, Time=0.24 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=2227.435, Time=0.06 sec
 ARIMA(0,1,3)(0,0,0)[0]             : AIC=2230.331, Time=0.12 sec
 ARIMA(2,1,1)(0,0,0)[0]             : AIC=2228.917, Time=0.15 sec
 ARIMA(2,1,3)(0,0,0)[0]             : AIC=2230.403, Time=0.35 sec

Best model:  ARIMA(1,1,2)(0,0,0)[0]          
Total fit time: 4.991 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=4249.011, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=4238.424, Time=0.06 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=4233.620, Time=0.17 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=4247.094, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=4205.804, Time=0.29 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=4205.993, Time=0.43 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=4206.924, Time=0.40 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=4213.342, Time=0.18 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=4238.396, Time=0.08 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=4182.583, Time=0.75 sec
 ARIMA(3,1,2)(0,0,0)[0] intercept   : AIC=4138.690, Time=0.90 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=4187.240, Time=0.56 sec
 ARIMA(4,1,2)(0,0,0)[0] intercept   : AIC=4131.721, Time=1.25 sec
 ARIMA(4,1,1)(0,0,0)[0] intercept   : AIC=4184.449, Time=0.75 sec
 ARIMA(5,1,2)(0,0,0)[0] intercept   : AIC=4126.813, Time=1.32 sec
 ARIMA(5,1,1)(0,0,0)[0] intercept   : AIC=4171.104, Time=0.53 sec
 ARIMA(6,1,2)(0,0,0)[0] intercept   : AIC=4132.682, Time=1.32 sec
 ARIMA(5,1,3)(0,0,0)[0] intercept   : AIC=4125.629, Time=1.34 sec
 ARIMA(4,1,3)(0,0,0)[0] intercept   : AIC=inf, Time=1.20 sec
 ARIMA(6,1,3)(0,0,0)[0] intercept   : AIC=4133.743, Time=1.54 sec
 ARIMA(5,1,4)(0,0,0)[0] intercept   : AIC=4101.288, Time=1.46 sec
 ARIMA(4,1,4)(0,0,0)[0] intercept   : AIC=4131.353, Time=1.30 sec
 ARIMA(6,1,4)(0,0,0)[0] intercept   : AIC=4101.097, Time=1.69 sec
 ARIMA(7,1,4)(0,0,0)[0] intercept   : AIC=4103.724, Time=1.81 sec
 ARIMA(6,1,5)(0,0,0)[0] intercept   : AIC=4103.301, Time=1.86 sec
 ARIMA(5,1,5)(0,0,0)[0] intercept   : AIC=4102.318, Time=1.81 sec
 ARIMA(7,1,3)(0,0,0)[0] intercept   : AIC=4123.176, Time=1.66 sec
 ARIMA(7,1,5)(0,0,0)[0] intercept   : AIC=4106.536, Time=1.99 sec
 ARIMA(6,1,4)(0,0,0)[0]             : AIC=4099.681, Time=1.36 sec
 ARIMA(5,1,4)(0,0,0)[0]             : AIC=4099.874, Time=1.28 sec
 ARIMA(6,1,3)(0,0,0)[0]             : AIC=4132.512, Time=0.98 sec
 ARIMA(7,1,4)(0,0,0)[0]             : AIC=4102.524, Time=1.68 sec
 ARIMA(6,1,5)(0,0,0)[0]             : AIC=4101.635, Time=1.59 sec
 ARIMA(5,1,3)(0,0,0)[0]             : AIC=4124.291, Time=0.95 sec
 ARIMA(5,1,5)(0,0,0)[0]             : AIC=4100.845, Time=1.49 sec
 ARIMA(7,1,3)(0,0,0)[0]             : AIC=4121.692, Time=1.24 sec
 ARIMA(7,1,5)(0,0,0)[0]             : AIC=4107.047, Time=1.86 sec

Best model:  ARIMA(6,1,4)(0,0,0)[0]          
Total fit time: 39.186 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=3266.344, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=3223.970, Time=0.11 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=inf, Time=0.27 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=3264.347, Time=0.02 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=3186.077, Time=0.13 sec
 ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=3177.518, Time=0.29 sec
 ARIMA(4,1,0)(0,0,0)[0] intercept   : AIC=3164.954, Time=0.39 sec
 ARIMA(5,1,0)(0,0,0)[0] intercept   : AIC=3108.323, Time=0.43 sec
 ARIMA(6,1,0)(0,0,0)[0] intercept   : AIC=3029.576, Time=0.42 sec
 ARIMA(7,1,0)(0,0,0)[0] intercept   : AIC=3023.320, Time=0.83 sec
 ARIMA(8,1,0)(0,0,0)[0] intercept   : AIC=3024.715, Time=0.67 sec
 ARIMA(7,1,1)(0,0,0)[0] intercept   : AIC=inf, Time=1.40 sec
 ARIMA(6,1,1)(0,0,0)[0] intercept   : AIC=3024.851, Time=0.93 sec
 ARIMA(8,1,1)(0,0,0)[0] intercept   : AIC=inf, Time=1.81 sec
 ARIMA(7,1,0)(0,0,0)[0]             : AIC=3021.329, Time=0.41 sec
 ARIMA(6,1,0)(0,0,0)[0]             : AIC=3027.582, Time=0.27 sec
 ARIMA(8,1,0)(0,0,0)[0]             : AIC=3022.722, Time=0.35 sec
 ARIMA(7,1,1)(0,0,0)[0]             : AIC=3010.968, Time=0.87 sec
 ARIMA(6,1,1)(0,0,0)[0]             : AIC=3022.860, Time=0.54 sec
 ARIMA(8,1,1)(0,0,0)[0]             : AIC=3010.714, Time=1.15 sec
 ARIMA(9,1,1)(0,0,0)[0]             : AIC=3008.223, Time=0.99 sec
 ARIMA(9,1,0)(0,0,0)[0]             : AIC=3024.674, Time=0.49 sec
 ARIMA(10,1,1)(0,0,0)[0]             : AIC=3008.277, Time=1.22 sec
 ARIMA(9,1,2)(0,0,0)[0]             : AIC=3004.865, Time=1.43 sec
 ARIMA(8,1,2)(0,0,0)[0]             : AIC=3015.003, Time=1.47 sec
 ARIMA(10,1,2)(0,0,0)[0]             : AIC=3009.606, Time=1.93 sec
 ARIMA(9,1,3)(0,0,0)[0]             : AIC=3007.631, Time=2.06 sec
 ARIMA(8,1,3)(0,0,0)[0]             : AIC=3008.899, Time=2.01 sec
 ARIMA(10,1,3)(0,0,0)[0]             : AIC=3012.007, Time=2.07 sec
 ARIMA(9,1,2)(0,0,0)[0] intercept   : AIC=3007.536, Time=2.43 sec

Best model:  ARIMA(9,1,2)(0,0,0)[0]          
Total fit time: 27.449 seconds
Performing stepwise search to minimize aic
 ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=2567.893, Time=0.03 sec
 ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=2554.270, Time=0.12 sec
 ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=2558.710, Time=0.16 sec
 ARIMA(0,0,0)(0,0,0)[0]             : AIC=2797.485, Time=0.02 sec
 ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=2543.486, Time=0.17 sec
 ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=2543.783, Time=0.27 sec
 ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=2532.808, Time=0.42 sec
 ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=2530.929, Time=0.32 sec
 ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=2532.815, Time=0.42 sec
 ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=2549.745, Time=0.24 sec
 ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=2532.013, Time=0.54 sec
 ARIMA(1,0,1)(0,0,0)[0]             : AIC=2537.320, Time=0.12 sec

Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept
Total fit time: 2.845 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2594.004, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2494.026, Time=0.09 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=inf, Time=0.34 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2592.004, Time=0.02 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=2446.125, Time=0.15 sec
 ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=2423.051, Time=0.19 sec
 ARIMA(4,1,0)(0,0,0)[0] intercept   : AIC=2411.875, Time=0.20 sec
 ARIMA(5,1,0)(0,0,0)[0] intercept   : AIC=2388.959, Time=0.26 sec
 ARIMA(6,1,0)(0,0,0)[0] intercept   : AIC=2351.219, Time=0.34 sec
 ARIMA(7,1,0)(0,0,0)[0] intercept   : AIC=2342.297, Time=0.39 sec
 ARIMA(8,1,0)(0,0,0)[0] intercept   : AIC=2338.133, Time=0.45 sec
 ARIMA(9,1,0)(0,0,0)[0] intercept   : AIC=2339.890, Time=0.61 sec
 ARIMA(8,1,1)(0,0,0)[0] intercept   : AIC=inf, Time=2.04 sec
 ARIMA(7,1,1)(0,0,0)[0] intercept   : AIC=inf, Time=1.00 sec
 ARIMA(9,1,1)(0,0,0)[0] intercept   : AIC=inf, Time=1.06 sec
 ARIMA(8,1,0)(0,0,0)[0]             : AIC=2336.170, Time=0.16 sec
 ARIMA(7,1,0)(0,0,0)[0]             : AIC=2340.327, Time=0.14 sec
 ARIMA(9,1,0)(0,0,0)[0]             : AIC=2337.929, Time=0.18 sec
 ARIMA(8,1,1)(0,0,0)[0]             : AIC=2326.231, Time=0.43 sec
 ARIMA(7,1,1)(0,0,0)[0]             : AIC=2327.733, Time=0.40 sec
 ARIMA(9,1,1)(0,0,0)[0]             : AIC=inf, Time=0.51 sec
 ARIMA(8,1,2)(0,0,0)[0]             : AIC=2328.415, Time=0.75 sec
 ARIMA(7,1,2)(0,0,0)[0]             : AIC=inf, Time=0.52 sec
 ARIMA(9,1,2)(0,0,0)[0]             : AIC=inf, Time=0.75 sec

Best model:  ARIMA(8,1,1)(0,0,0)[0]          
Total fit time: 11.013 seconds
Performing stepwise search to minimize aic
 ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=2768.540, Time=0.01 sec
 ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=2766.785, Time=0.06 sec
 ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=2767.106, Time=0.07 sec
 ARIMA(0,0,0)(0,0,0)[0]             : AIC=3074.569, Time=0.01 sec
 ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=2767.688, Time=0.08 sec
 ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=2764.818, Time=0.25 sec
 ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=2766.808, Time=0.26 sec
 ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=2766.806, Time=0.24 sec
 ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=2768.594, Time=0.08 sec
 ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=2767.778, Time=0.38 sec
 ARIMA(1,0,1)(0,0,0)[0]             : AIC=2777.475, Time=0.09 sec

Best model:  ARIMA(1,0,1)(0,0,0)[0] intercept
Total fit time: 1.515 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2857.321, Time=0.01 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2787.185, Time=0.04 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2714.781, Time=0.06 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2855.324, Time=0.01 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2708.049, Time=0.13 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=inf, Time=0.29 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=2709.544, Time=0.21 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=2709.546, Time=0.09 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=2777.898, Time=0.08 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=2709.621, Time=0.21 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=2706.218, Time=0.05 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=2712.870, Time=0.02 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=2785.188, Time=0.02 sec
 ARIMA(2,1,1)(0,0,0)[0]             : AIC=2707.030, Time=0.18 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=2707.736, Time=0.10 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=2707.685, Time=0.04 sec
 ARIMA(2,1,0)(0,0,0)[0]             : AIC=2775.904, Time=0.03 sec
 ARIMA(2,1,2)(0,0,0)[0]             : AIC=2707.833, Time=0.12 sec

Best model:  ARIMA(1,1,1)(0,0,0)[0]          
Total fit time: 1.704 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=3170.979, Time=0.01 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=3128.186, Time=0.05 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=3046.571, Time=0.07 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=3168.982, Time=0.01 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=3032.753, Time=0.12 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=3033.979, Time=0.16 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=3034.386, Time=0.20 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=3032.922, Time=0.10 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=3114.632, Time=0.13 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=inf, Time=0.37 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=3030.753, Time=0.05 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=3044.574, Time=0.02 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=3126.191, Time=0.03 sec
 ARIMA(2,1,1)(0,0,0)[0]             : AIC=3031.979, Time=0.09 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=3032.386, Time=0.10 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=3030.922, Time=0.05 sec
 ARIMA(2,1,0)(0,0,0)[0]             : AIC=3112.639, Time=0.05 sec
 ARIMA(2,1,2)(0,0,0)[0]             : AIC=inf, Time=0.31 sec

Best model:  ARIMA(1,1,1)(0,0,0)[0]          
Total fit time: 1.934 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=3695.851, Time=0.01 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=3694.372, Time=0.02 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=3692.813, Time=0.06 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=3694.404, Time=0.01 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=3681.456, Time=0.15 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=3678.468, Time=0.19 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=3689.757, Time=0.07 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=3674.957, Time=0.26 sec
 ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=3682.790, Time=0.10 sec
 ARIMA(4,1,1)(0,0,0)[0] intercept   : AIC=3667.113, Time=0.20 sec
 ARIMA(4,1,0)(0,0,0)[0] intercept   : AIC=3665.379, Time=0.13 sec
 ARIMA(5,1,0)(0,0,0)[0] intercept   : AIC=3667.153, Time=0.19 sec
 ARIMA(5,1,1)(0,0,0)[0] intercept   : AIC=3669.105, Time=0.27 sec
 ARIMA(4,1,0)(0,0,0)[0]             : AIC=3665.227, Time=0.08 sec
 ARIMA(3,1,0)(0,0,0)[0]             : AIC=3681.919, Time=0.05 sec
 ARIMA(5,1,0)(0,0,0)[0]             : AIC=3667.096, Time=0.10 sec
 ARIMA(4,1,1)(0,0,0)[0]             : AIC=3667.067, Time=0.13 sec
 ARIMA(3,1,1)(0,0,0)[0]             : AIC=3674.729, Time=0.11 sec
 ARIMA(5,1,1)(0,0,0)[0]             : AIC=3669.064, Time=0.18 sec

Best model:  ARIMA(4,1,0)(0,0,0)[0]          
Total fit time: 2.316 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=3740.639, Time=0.01 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=3684.192, Time=0.08 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=3655.189, Time=0.07 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=3738.640, Time=0.01 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=3642.652, Time=0.15 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=inf, Time=0.25 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=3654.750, Time=0.18 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=3650.402, Time=0.14 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=3669.084, Time=0.11 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=3646.632, Time=0.23 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=3646.078, Time=0.07 sec

Best model:  ARIMA(1,1,1)(0,0,0)[0] intercept
Total fit time: 1.314 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=3849.076, Time=0.01 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=3802.844, Time=0.05 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=3719.353, Time=0.05 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=3847.085, Time=0.01 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=3706.728, Time=0.09 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=3708.279, Time=0.14 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=3708.484, Time=0.19 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=3706.790, Time=0.09 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=3787.504, Time=0.13 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=3710.683, Time=0.15 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=3704.999, Time=0.06 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=3717.547, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=3800.850, Time=0.03 sec
 ARIMA(2,1,1)(0,0,0)[0]             : AIC=3706.542, Time=0.10 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=3706.752, Time=0.10 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=3705.050, Time=0.05 sec
 ARIMA(2,1,0)(0,0,0)[0]             : AIC=3785.510, Time=0.04 sec
 ARIMA(2,1,2)(0,0,0)[0]             : AIC=3708.952, Time=0.12 sec

Best model:  ARIMA(1,1,1)(0,0,0)[0]          
Total fit time: 1.476 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2836.495, Time=0.01 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2723.898, Time=0.05 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2631.301, Time=0.05 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2834.495, Time=0.01 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2632.099, Time=0.08 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=2632.139, Time=0.07 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=2632.599, Time=0.10 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=2629.465, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=2630.231, Time=0.04 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=2630.270, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=2721.898, Time=0.02 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=2630.773, Time=0.06 sec

Best model:  ARIMA(0,1,1)(0,0,0)[0]          
Total fit time: 0.544 seconds
Performing stepwise search to minimize aic
 ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=1997.391, Time=0.01 sec
 ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=1799.119, Time=0.03 sec
 ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=1855.272, Time=0.04 sec
 ARIMA(0,0,0)(0,0,0)[0]             : AIC=2004.016, Time=0.01 sec
 ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=1798.751, Time=0.05 sec
 ARIMA(3,0,0)(0,0,0)[0] intercept   : AIC=1798.996, Time=0.06 sec
 ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=1801.445, Time=0.17 sec
 ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=1799.266, Time=0.06 sec
 ARIMA(3,0,1)(0,0,0)[0] intercept   : AIC=1798.950, Time=0.11 sec
 ARIMA(2,0,0)(0,0,0)[0]             : AIC=1798.759, Time=0.03 sec

Best model:  ARIMA(2,0,0)(0,0,0)[0] intercept
Total fit time: 0.558 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=3277.566, Time=0.01 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=3209.211, Time=0.09 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=3102.421, Time=0.05 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=3275.566, Time=0.01 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=3103.186, Time=0.07 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=3102.967, Time=0.08 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=3101.034, Time=0.16 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=3102.683, Time=0.18 sec
 ARIMA(1,1,3)(0,0,0)[0] intercept   : AIC=3102.721, Time=0.21 sec
 ARIMA(0,1,3)(0,0,0)[0] intercept   : AIC=3103.045, Time=0.11 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=3103.778, Time=0.14 sec
 ARIMA(2,1,3)(0,0,0)[0] intercept   : AIC=3104.556, Time=0.41 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=3099.196, Time=0.07 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=3101.139, Time=0.04 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=3101.356, Time=0.05 sec
 ARIMA(2,1,2)(0,0,0)[0]             : AIC=3100.830, Time=0.13 sec
 ARIMA(1,1,3)(0,0,0)[0]             : AIC=3100.869, Time=0.12 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=3100.566, Time=0.02 sec
 ARIMA(0,1,3)(0,0,0)[0]             : AIC=3101.182, Time=0.06 sec
 ARIMA(2,1,1)(0,0,0)[0]             : AIC=3101.915, Time=0.08 sec
 ARIMA(2,1,3)(0,0,0)[0]             : AIC=3102.708, Time=0.34 sec

Best model:  ARIMA(1,1,2)(0,0,0)[0]          
Total fit time: 2.432 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2983.292, Time=0.01 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2871.569, Time=0.06 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2792.319, Time=0.07 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2981.292, Time=0.01 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2794.178, Time=0.11 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=2794.196, Time=0.08 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=2795.205, Time=0.14 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=2790.605, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=2792.447, Time=0.04 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=2792.467, Time=0.04 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=2869.570, Time=0.01 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=2793.466, Time=0.07 sec

Best model:  ARIMA(0,1,1)(0,0,0)[0]          
Total fit time: 0.681 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2828.003, Time=0.01 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2749.845, Time=0.04 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2652.810, Time=0.04 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2826.020, Time=0.01 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2653.735, Time=0.07 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=2653.690, Time=0.07 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=inf, Time=0.29 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=2652.641, Time=0.03 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=2653.723, Time=0.04 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=2653.676, Time=0.05 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=2747.907, Time=0.02 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=inf, Time=0.21 sec

Best model:  ARIMA(0,1,1)(0,0,0)[0]          
Total fit time: 0.902 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2932.055, Time=0.01 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2850.398, Time=0.04 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2734.649, Time=0.06 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2930.055, Time=0.01 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2736.643, Time=0.08 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=2736.642, Time=0.07 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=2738.647, Time=0.09 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=2732.774, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=2734.769, Time=0.05 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=2734.768, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=2848.398, Time=0.02 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=2736.772, Time=0.05 sec

Best model:  ARIMA(0,1,1)(0,0,0)[0]          
Total fit time: 0.555 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2723.212, Time=0.01 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2588.926, Time=0.05 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2518.601, Time=0.04 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2721.212, Time=0.01 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2518.839, Time=0.08 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=2519.224, Time=0.07 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=2519.469, Time=0.11 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=2516.601, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=2516.839, Time=0.06 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=2517.224, Time=0.04 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=2586.926, Time=0.02 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=2517.469, Time=0.06 sec

Best model:  ARIMA(0,1,1)(0,0,0)[0]          
Total fit time: 0.577 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2595.168, Time=0.01 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2518.297, Time=0.04 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2410.902, Time=0.04 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2593.168, Time=0.01 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2412.579, Time=0.11 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=2412.533, Time=0.07 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=2414.166, Time=0.15 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=2408.902, Time=0.03 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=2410.579, Time=0.05 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=2410.533, Time=0.05 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=2516.297, Time=0.03 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=2412.166, Time=0.09 sec

Best model:  ARIMA(0,1,1)(0,0,0)[0]          
Total fit time: 0.694 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=2884.760, Time=0.01 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2838.736, Time=0.04 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2720.576, Time=0.08 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=2882.760, Time=0.01 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=2715.389, Time=0.13 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=2713.033, Time=0.15 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=2807.078, Time=0.08 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=2712.981, Time=0.17 sec
 ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=2784.642, Time=0.08 sec
 ARIMA(4,1,1)(0,0,0)[0] intercept   : AIC=2713.937, Time=0.23 sec
 ARIMA(3,1,2)(0,0,0)[0] intercept   : AIC=2713.431, Time=0.28 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=2711.932, Time=0.33 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=2715.264, Time=0.15 sec
 ARIMA(2,1,3)(0,0,0)[0] intercept   : AIC=2710.845, Time=0.33 sec
 ARIMA(1,1,3)(0,0,0)[0] intercept   : AIC=2713.760, Time=0.35 sec
 ARIMA(3,1,3)(0,0,0)[0] intercept   : AIC=2714.769, Time=0.50 sec
 ARIMA(2,1,4)(0,0,0)[0] intercept   : AIC=2712.845, Time=0.40 sec
 ARIMA(1,1,4)(0,0,0)[0] intercept   : AIC=2714.040, Time=0.23 sec
 ARIMA(3,1,4)(0,0,0)[0] intercept   : AIC=2713.761, Time=0.53 sec
 ARIMA(2,1,3)(0,0,0)[0]             : AIC=2708.927, Time=0.21 sec
 ARIMA(1,1,3)(0,0,0)[0]             : AIC=2711.808, Time=0.29 sec
 ARIMA(2,1,2)(0,0,0)[0]             : AIC=2709.972, Time=0.24 sec
 ARIMA(3,1,3)(0,0,0)[0]             : AIC=2709.573, Time=0.36 sec
 ARIMA(2,1,4)(0,0,0)[0]             : AIC=2710.926, Time=0.30 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=2713.350, Time=0.10 sec
 ARIMA(1,1,4)(0,0,0)[0]             : AIC=2712.085, Time=0.18 sec
 ARIMA(3,1,2)(0,0,0)[0]             : AIC=2711.468, Time=0.27 sec
 ARIMA(3,1,4)(0,0,0)[0]             : AIC=2711.816, Time=0.40 sec

Best model:  ARIMA(2,1,3)(0,0,0)[0]          
Total fit time: 6.435 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=3008.357, Time=0.01 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=2987.978, Time=0.04 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=2891.598, Time=0.09 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=3006.357, Time=0.01 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=inf, Time=0.23 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=inf, Time=0.21 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=inf, Time=0.30 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=2889.601, Time=0.03 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=2865.911, Time=0.06 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=2985.978, Time=0.03 sec
 ARIMA(2,1,1)(0,0,0)[0]             : AIC=2857.696, Time=0.09 sec
 ARIMA(2,1,0)(0,0,0)[0]             : AIC=2956.233, Time=0.02 sec
 ARIMA(3,1,1)(0,0,0)[0]             : AIC=2857.721, Time=0.13 sec
 ARIMA(2,1,2)(0,0,0)[0]             : AIC=2850.007, Time=0.18 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=2860.445, Time=0.09 sec
 ARIMA(3,1,2)(0,0,0)[0]             : AIC=2861.456, Time=0.25 sec
 ARIMA(2,1,3)(0,0,0)[0]             : AIC=2794.774, Time=0.39 sec
 ARIMA(1,1,3)(0,0,0)[0]             : AIC=2859.594, Time=0.24 sec
 ARIMA(3,1,3)(0,0,0)[0]             : AIC=2853.848, Time=0.30 sec
 ARIMA(2,1,4)(0,0,0)[0]             : AIC=inf, Time=0.62 sec
 ARIMA(1,1,4)(0,0,0)[0]             : AIC=2860.187, Time=0.17 sec
 ARIMA(3,1,4)(0,0,0)[0]             : AIC=inf, Time=0.56 sec
 ARIMA(2,1,3)(0,0,0)[0] intercept   : AIC=2796.644, Time=0.46 sec

Best model:  ARIMA(2,1,3)(0,0,0)[0]          
Total fit time: 4.518 seconds
In [70]:
plotARIMAfunc(train_df_dundee, test_df_dundee, fit_df_dundee, forecast_df_dundee, lower_df_dundee, upper_df_dundee)
RMSE for ***TEST SITE*** Charge Your Car HQ Stations: 13.72907031779763
RMSE for Ardler Complex, Dundee Stations: 8.685406417161747
RMSE for Balunie Drive, Dundee Stations: 14.431368470096057
RMSE for Brington Place Sheltered Housing, Dundee Stations: 5.032932687422627
RMSE for DCC Environment, 34 Harefield Road Stations: 3.2930921132329536e-05
RMSE for Dock Street, Dundee Stations: 21.02145175602944
RMSE for Dundee House, Dundee Stations: 266.8385088781542
RMSE for Dundee Ice Arena, Dundee Stations: 101.82604186357524
RMSE for Earn Cresent, Dundee Stations: 0.06286407814376119
RMSE for Gellatly Street Car Park, Dundee Stations: 26.465802611983094
RMSE for Greenmarket Multi Car Park, Dundee Stations: 42.85239838509775
RMSE for Housing Office East, Dundee Stations: 18.487433778364913
RMSE for Housing Office West, Dundee Stations: 10.687982771081426
RMSE for Janet Brougham House, Dundee Stations: 4.972380071165433e-05
RMSE for Lochee Charging Hub, Dundee Stations: 266.53964299479054
RMSE for Marchbanks, Dundee Stations: 22.112810812087943
RMSE for Menziehill House, Dundee Stations: 9.242159960879269
RMSE for Mitchell Street, Dundee Stations: 4.52652238134178
RMSE for Nethergate, Dundee Stations: 12.649834624521548
RMSE for Oakland Day Centre, Dundee Stations: 9.791448103063336
RMSE for Olympia Multi-Storey Car Park, Dundee Stations: 16.5176569008321
RMSE for Princes Street Charging Hub Stations: 245.74283795308918
RMSE for Public Works Dept, Clepington Rd. Dundee Stations: 47.050493956588575
RMSE for Queen Street Car Park, Broughty Ferry, Dundee Stations: 60.14782368232508
RMSE for Sinclair Street Stations: 3.5431039996844804e-10
RMSE for Sinclair Street, Dundee Stations: 0.6641645528581733
RMSE for Social Work Building, Jack Martin Way, Dundee Stations: 7.594767160131575
RMSE for South Tay Street Stations: 3.809719802964983e-11
RMSE for South Tay Street, Dundee Stations: 18.386813414035576
RMSE for Trades Lane Stations: 5.979936798238124e-08
RMSE for Trades Lane, Dundee Stations: 0.06399750075769692
RMSE for Turriff House Rannoch Road, Dundee Stations: 7.722791914761989
RMSE for University of Dundee, Nethergate, Dundee Stations: 1.6642761033885702
RMSE for Whitfield Centre, Dundee Stations: 24.110184088487763
No description has been provided for this image

Perth¶

In [71]:
df_1 = pd.read_csv('data/EV_ChargeStation_Use_Sept_2016_to_Aug_2017.csv', index_col=[0]).drop(columns=['OBJECTID'])
df_2 = pd.read_csv('data/EVChargeStationUseSept2017toAug2018.csv', index_col=[0])
df_3 = pd.read_csv('data/EVChargeStationUseSept2018toAug2019.csv', index_col=[0])

df_1 = df_1[df_1['Site'] != '***TEST SITE*** Charge Your Car HQ']
df_3 = df_3[df_3['Site'] != '***TEST SITE*** Charge Your Car HQ']
In [72]:
# Define a mapping dictionary for renaming
rename_mapping = {
    'King Street Car Park, Crieff': 'King Street Car Park',
    'Broxden Park & Ride, Perth': 'Broxden Park & Ride',
    'Canal Street Car Park 3rd floor, Perth': 'Canal Street Car Park',
    'Canal Street Car Park 3rd floor ': 'Canal Street Car Park',
    'Friarton Depot, Perth': 'Friarton Depot',
    'South Inch Car Park, Perth': 'South Inch Car Park',
    'Kinross Park and Ride, Kinross': 'Kinross Park and Ride',
    ' Leslie Street Car Park, Blairgowrie': 'Leslie Street Car Park, Blairgowrie',
}

# Replace the values in the 'Site' column using the mapping
df_1['Site'] = df_1['Site'].replace(rename_mapping)
df_2['Site'] = df_2['Site'].replace(rename_mapping)
df_3['Site'] = df_3['Site'].replace(rename_mapping)

df_1 = df_1.rename(columns={
    'CP_ID': 'CP ID',
    'Start_Date': 'Start Date',
    'Start_Time': 'Start Time',
    'End_Date': 'End Date',
    'End_Time': 'End Time',
    'Total_kWh': 'Total kWh'
})

# Union data
data_perth = pd.concat([df_1, df_2, df_3]).drop_duplicates()

# Drop records with below 0 Total kWh
data_perth = data_perth[data_perth['Total kWh'] >= 0]

# Drop two stations (too little data)
data_perth = data_perth[data_perth['Site'] != 'Market Square Alyth']
data_perth = data_perth[data_perth['Site'] != 'Mill Street, Perth']
In [73]:
data_perth.head()
Out[73]:
CP ID Connector Start Date Start Time End Date End Time Total kWh Site Model
_id
1 51519 2 2017/08/31 00:00:00 22:12:00 2017/08/31 00:00:00 23:11:00 18.27 Broxden Park & Ride APT Triple Rapid Charger
2 51250 1 2017/08/31 00:00:00 22:01:00 2017/08/31 00:00:00 22:31:00 19.45 Crown Inn Wynd Car Park, Auchterarder Siemens Triple Rapid Charger
3 50575 2 2017/08/31 00:00:00 21:21:00 2017/08/31 00:00:00 21:59:00 19.71 South Inch Car Park APT Triple Rapid Charger
4 51516 2 2017/08/31 00:00:00 20:43:00 2017/08/31 00:00:00 21:03:00 9.84 Kinross Park and Ride APT Triple Rapid Charger
5 50994 2 2017/08/31 00:00:00 19:50:00 2017/08/31 00:00:00 20:50:00 14.17 Leslie Street Car Park, Blairgowrie APT Triple Rapid Charger
In [74]:
data_perth = data_perth.assign(timestamp=pd.to_datetime(data_perth["Start Date"]).dt.date)
data_perth = data_perth[["timestamp", "Site", "Total kWh"]].groupby(["timestamp", "Site"], as_index=False).sum()
data_perth = pd.pivot_table(data_perth, values="Total kWh", index="timestamp", columns= "Site", aggfunc=np.sum, fill_value=0)
data_perth.reset_index(inplace=True)
In [75]:
data_perth
Out[75]:
Site timestamp Atholl Street Car Park, Dunkeld Broxden Park & Ride Canal Street Car Park Crown Inn Wynd Car Park, Auchterarder Friarton Depot King Street Car Park Kinross Park and Ride Leslie Street Car Park, Blairgowrie Moness Terrace Car Park, Aberfeldy Rie-Achan Road Car Park, Pitlochry South Inch Car Park
0 2016-01-09 0.000 111.820 0.000 0.000 35.370 0.000 42.435 13.234 0.000 40.436 23.946
1 2016-01-10 0.000 134.360 0.000 0.380 0.000 25.172 83.798 0.000 42.324 44.970 43.408
2 2016-01-11 0.000 90.670 0.000 0.000 35.930 100.149 68.370 35.475 0.000 19.590 35.115
3 2016-01-12 0.000 105.014 0.000 0.000 45.780 4.030 134.090 61.890 6.800 20.240 10.278
4 2016-02-09 0.000 59.211 0.000 5.820 0.000 0.000 56.630 9.540 0.000 18.610 36.482
... ... ... ... ... ... ... ... ... ... ... ... ...
1090 2019-12-04 39.174 198.414 10.064 35.979 47.753 31.058 116.072 0.000 90.670 107.430 100.320
1091 2019-12-05 59.682 107.571 0.000 49.180 0.000 83.894 236.344 5.822 149.029 45.470 54.210
1092 2019-12-06 29.338 189.394 50.008 73.523 72.499 72.792 263.845 29.646 38.923 100.370 100.715
1093 2019-12-07 15.440 342.782 30.845 55.829 20.380 33.170 227.842 8.430 84.198 177.090 101.669
1094 2019-12-08 67.789 227.317 37.519 112.902 34.740 106.708 295.120 59.715 55.391 71.044 33.350

1095 rows × 12 columns

In [76]:
print(data_perth[data_perth == 0].count(axis=0)/len(data_perth.index))
Site
timestamp                                0.000000
Atholl Street Car Park, Dunkeld          0.369863
Broxden Park & Ride                      0.000000
Canal Street Car Park                    0.187215
Crown Inn Wynd Car Park, Auchterarder    0.103196
Friarton Depot                           0.210959
King Street Car Park                     0.053881
Kinross Park and Ride                    0.003653
Leslie Street Car Park, Blairgowrie      0.075799
Moness Terrace Car Park, Aberfeldy       0.136986
Rie-Achan Road Car Park, Pitlochry       0.037443
South Inch Car Park                      0.008219
dtype: float64
In [77]:
train_df_perth, test_df_perth, fit_df_perth, forecast_df_perth, lower_df_perth, upper_df_perth = autoARIMAfunc(data_perth)
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=10030.742, Time=0.02 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=9811.805, Time=0.09 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=9518.750, Time=0.13 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=10028.747, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=9493.592, Time=0.31 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=9494.064, Time=0.57 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=inf, Time=0.93 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=9495.736, Time=0.29 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=9688.353, Time=0.16 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=9495.704, Time=0.61 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=9495.701, Time=0.11 sec

Best model:  ARIMA(1,1,1)(0,0,0)[0] intercept
Total fit time: 3.232 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=12032.604, Time=0.02 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=11765.218, Time=0.11 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=11493.862, Time=0.17 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=12030.605, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=11473.533, Time=0.31 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=11467.721, Time=0.49 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=11699.774, Time=0.06 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=11469.337, Time=0.62 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=11469.393, Time=0.59 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=11493.244, Time=0.28 sec
 ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=11651.560, Time=0.10 sec
 ARIMA(3,1,2)(0,0,0)[0] intercept   : AIC=11469.468, Time=0.59 sec
 ARIMA(2,1,1)(0,0,0)[0]             : AIC=11470.368, Time=0.20 sec

Best model:  ARIMA(2,1,1)(0,0,0)[0] intercept
Total fit time: 3.554 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=9762.363, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=9515.295, Time=0.10 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=9145.777, Time=0.18 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=9760.363, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=9142.473, Time=0.27 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=9144.369, Time=0.34 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=9144.344, Time=0.38 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=9142.385, Time=0.27 sec
 ARIMA(0,1,3)(0,0,0)[0] intercept   : AIC=9144.352, Time=0.35 sec
 ARIMA(1,1,3)(0,0,0)[0] intercept   : AIC=9146.380, Time=0.39 sec
 ARIMA(0,1,2)(0,0,0)[0]             : AIC=9143.411, Time=0.09 sec

Best model:  ARIMA(0,1,2)(0,0,0)[0] intercept
Total fit time: 2.422 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=10637.850, Time=0.02 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=10324.212, Time=0.11 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=9982.715, Time=0.15 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=10635.857, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=9983.967, Time=0.28 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=9984.033, Time=0.28 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=9986.351, Time=0.42 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=9982.903, Time=0.04 sec

Best model:  ARIMA(0,1,1)(0,0,0)[0] intercept
Total fit time: 1.316 seconds
Performing stepwise search to minimize aic
 ARIMA(0,0,0)(0,0,0)[0] intercept   : AIC=9120.514, Time=0.01 sec
 ARIMA(1,0,0)(0,0,0)[0] intercept   : AIC=9109.434, Time=0.04 sec
 ARIMA(0,0,1)(0,0,0)[0] intercept   : AIC=9108.063, Time=0.18 sec
 ARIMA(0,0,0)(0,0,0)[0]             : AIC=10083.023, Time=0.01 sec
 ARIMA(1,0,1)(0,0,0)[0] intercept   : AIC=9106.086, Time=0.30 sec
 ARIMA(2,0,1)(0,0,0)[0] intercept   : AIC=9107.265, Time=0.57 sec
 ARIMA(1,0,2)(0,0,0)[0] intercept   : AIC=9107.262, Time=0.51 sec
 ARIMA(0,0,2)(0,0,0)[0] intercept   : AIC=9107.887, Time=0.20 sec
 ARIMA(2,0,0)(0,0,0)[0] intercept   : AIC=9109.159, Time=0.11 sec
 ARIMA(2,0,2)(0,0,0)[0] intercept   : AIC=9099.778, Time=0.98 sec
 ARIMA(3,0,2)(0,0,0)[0] intercept   : AIC=9108.466, Time=0.43 sec
 ARIMA(2,0,3)(0,0,0)[0] intercept   : AIC=9101.676, Time=1.06 sec
 ARIMA(1,0,3)(0,0,0)[0] intercept   : AIC=9097.091, Time=0.83 sec
 ARIMA(0,0,3)(0,0,0)[0] intercept   : AIC=9106.576, Time=0.23 sec
 ARIMA(1,0,4)(0,0,0)[0] intercept   : AIC=9098.405, Time=1.02 sec
 ARIMA(0,0,4)(0,0,0)[0] intercept   : AIC=9107.527, Time=0.40 sec
 ARIMA(2,0,4)(0,0,0)[0] intercept   : AIC=inf, Time=1.22 sec
 ARIMA(1,0,3)(0,0,0)[0]             : AIC=9110.793, Time=0.42 sec

Best model:  ARIMA(1,0,3)(0,0,0)[0] intercept
Total fit time: 8.518 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=11353.305, Time=0.02 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=11142.981, Time=0.09 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=10780.862, Time=0.23 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=11351.305, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=inf, Time=0.38 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=inf, Time=0.38 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=10766.075, Time=0.35 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=10761.116, Time=0.48 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=inf, Time=0.79 sec
 ARIMA(3,1,2)(0,0,0)[0] intercept   : AIC=inf, Time=0.69 sec
 ARIMA(2,1,3)(0,0,0)[0] intercept   : AIC=inf, Time=0.84 sec
 ARIMA(1,1,3)(0,0,0)[0] intercept   : AIC=10761.554, Time=0.63 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=inf, Time=0.48 sec
 ARIMA(3,1,3)(0,0,0)[0] intercept   : AIC=10764.544, Time=1.10 sec
 ARIMA(2,1,2)(0,0,0)[0]             : AIC=10765.260, Time=0.31 sec

Best model:  ARIMA(2,1,2)(0,0,0)[0] intercept
Total fit time: 6.765 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=11805.941, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=11550.350, Time=0.06 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=11320.050, Time=0.14 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=11803.941, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=11290.265, Time=0.32 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=11281.184, Time=0.35 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=11477.699, Time=0.06 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=11282.657, Time=0.48 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=11282.225, Time=0.86 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=11280.668, Time=0.52 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=11296.598, Time=0.29 sec
 ARIMA(1,1,3)(0,0,0)[0] intercept   : AIC=11282.251, Time=0.93 sec
 ARIMA(0,1,3)(0,0,0)[0] intercept   : AIC=11285.276, Time=0.42 sec
 ARIMA(2,1,3)(0,0,0)[0] intercept   : AIC=11281.473, Time=0.99 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=11287.691, Time=0.26 sec

Best model:  ARIMA(1,1,2)(0,0,0)[0] intercept
Total fit time: 5.762 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=10400.723, Time=0.02 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=10163.676, Time=0.07 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=9887.935, Time=0.12 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=10398.725, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=9869.780, Time=0.23 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=9869.747, Time=0.35 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=10091.309, Time=0.07 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=9871.112, Time=0.47 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=9871.461, Time=0.65 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=9870.381, Time=0.35 sec
 ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=10046.114, Time=0.11 sec
 ARIMA(3,1,2)(0,0,0)[0] intercept   : AIC=9873.747, Time=0.39 sec
 ARIMA(2,1,1)(0,0,0)[0]             : AIC=9868.433, Time=0.18 sec
 ARIMA(1,1,1)(0,0,0)[0]             : AIC=9868.434, Time=0.11 sec
 ARIMA(2,1,0)(0,0,0)[0]             : AIC=10089.319, Time=0.04 sec
 ARIMA(3,1,1)(0,0,0)[0]             : AIC=9869.781, Time=0.29 sec
 ARIMA(2,1,2)(0,0,0)[0]             : AIC=9870.141, Time=0.38 sec
 ARIMA(1,1,0)(0,0,0)[0]             : AIC=10161.682, Time=0.03 sec
 ARIMA(1,1,2)(0,0,0)[0]             : AIC=9869.061, Time=0.21 sec
 ARIMA(3,1,0)(0,0,0)[0]             : AIC=10044.123, Time=0.07 sec
 ARIMA(3,1,2)(0,0,0)[0]             : AIC=9872.433, Time=0.25 sec

Best model:  ARIMA(2,1,1)(0,0,0)[0]          
Total fit time: 4.409 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=10634.333, Time=0.02 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=10327.814, Time=0.07 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=9942.499, Time=0.19 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=10632.334, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=9944.307, Time=0.27 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=9944.314, Time=0.26 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=9946.487, Time=0.25 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=9945.072, Time=0.06 sec

Best model:  ARIMA(0,1,1)(0,0,0)[0] intercept
Total fit time: 1.143 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=11473.581, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=11148.381, Time=0.09 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=10861.176, Time=0.16 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=11471.581, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=10858.734, Time=0.33 sec
 ARIMA(2,1,1)(0,0,0)[0] intercept   : AIC=10849.066, Time=0.72 sec
 ARIMA(2,1,0)(0,0,0)[0] intercept   : AIC=11055.925, Time=0.08 sec
 ARIMA(3,1,1)(0,0,0)[0] intercept   : AIC=10849.518, Time=0.82 sec
 ARIMA(2,1,2)(0,0,0)[0] intercept   : AIC=10861.988, Time=0.52 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=10862.543, Time=0.31 sec
 ARIMA(3,1,0)(0,0,0)[0] intercept   : AIC=11035.948, Time=0.08 sec
 ARIMA(3,1,2)(0,0,0)[0] intercept   : AIC=10845.396, Time=0.67 sec
 ARIMA(4,1,2)(0,0,0)[0] intercept   : AIC=10846.827, Time=0.77 sec
 ARIMA(3,1,3)(0,0,0)[0] intercept   : AIC=10847.006, Time=0.70 sec
 ARIMA(2,1,3)(0,0,0)[0] intercept   : AIC=10848.396, Time=0.90 sec
 ARIMA(4,1,1)(0,0,0)[0] intercept   : AIC=10846.639, Time=0.93 sec
 ARIMA(4,1,3)(0,0,0)[0] intercept   : AIC=10848.777, Time=1.20 sec
 ARIMA(3,1,2)(0,0,0)[0]             : AIC=10845.774, Time=0.36 sec

Best model:  ARIMA(3,1,2)(0,0,0)[0] intercept
Total fit time: 8.696 seconds
Performing stepwise search to minimize aic
 ARIMA(0,1,0)(0,0,0)[0] intercept   : AIC=11115.758, Time=0.03 sec
 ARIMA(1,1,0)(0,0,0)[0] intercept   : AIC=10819.519, Time=0.14 sec
 ARIMA(0,1,1)(0,0,0)[0] intercept   : AIC=10436.160, Time=0.28 sec
 ARIMA(0,1,0)(0,0,0)[0]             : AIC=11113.760, Time=0.02 sec
 ARIMA(1,1,1)(0,0,0)[0] intercept   : AIC=10437.169, Time=0.51 sec
 ARIMA(0,1,2)(0,0,0)[0] intercept   : AIC=10437.208, Time=0.43 sec
 ARIMA(1,1,2)(0,0,0)[0] intercept   : AIC=10439.555, Time=0.46 sec
 ARIMA(0,1,1)(0,0,0)[0]             : AIC=10438.854, Time=0.07 sec

Best model:  ARIMA(0,1,1)(0,0,0)[0] intercept
Total fit time: 1.943 seconds
In [78]:
plotARIMAfunc(train_df_perth, test_df_perth, fit_df_perth, forecast_df_perth, lower_df_perth, upper_df_perth)
RMSE for Atholl Street Car Park, Dunkeld Stations: 57.56484821375761
RMSE for Broxden Park & Ride Stations: 72.02142375123651
RMSE for Canal Street Car Park Stations: 21.910401718878102
RMSE for Crown Inn Wynd Car Park, Auchterarder Stations: 34.11999425969723
RMSE for Friarton Depot Stations: 19.21460844219384
RMSE for King Street Car Park Stations: 36.018682504483664
RMSE for Kinross Park and Ride Stations: 61.77410729734898
RMSE for Leslie Street Car Park, Blairgowrie Stations: 38.43702496064899
RMSE for Moness Terrace Car Park, Aberfeldy Stations: 37.22802828762869
RMSE for Rie-Achan Road Car Park, Pitlochry Stations: 50.55069573338147
RMSE for South Inch Car Park Stations: 40.86241878616647
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